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FRM Part I · FRM Exam Part I · Bond Yields and Return Calculations

For a given maturity beyond one year, the spot curve is upward sloping. Which ordering of the par yield, the spot rate and the instantaneous forward rate for that maturity is correct?

With an upward-sloping spot curve, the forward rate is highest, then the spot rate, then the par yield. The spot rate averages lower earlier forward rates, and the par yield is lower still because early coupons are discounted at lower short-term spot rates.

  1. AForward rate > spot rate > par yieldCorrect
  2. BPar yield > spot rate > forward rate
  3. CSpot rate > forward rate > par yield
  4. DSpot rate > par yield > forward rate

Explanation

When the spot curve slopes upward, the forward rate lies above the spot rate, because the spot rate is an average of earlier forwards. The par yield lies below the spot rate, because coupons are received earlier and are discounted at lower short-dated spot rates. So the ordering is forward > spot > par yield. The reverse ordering applies when the curve is downward sloping.

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